Search

Comparative lifetime experiments are remarkable when the study is to ascertain the relative merits of two competing products regarding the duration of their service life. This paper considers the comparative lifetime experiments of two Gompertz populations under a balanced joint progressive Type-II censoring scheme. The lifetime distributions of the units are assumed to follow the Gompertz distribution with a common shape but different scale parameters. The maximum likelihood estimates of the unknown parameters are derived. The existence of the maximum likelihood estimates is proved. Expectation-maximization and stochastic expectation-maximization algorithms are provided to calculate the estimates. The bootstrap-p, bootstrap-t, and approximate confidence intervals are established. To obtain the Bayesian estimates, it is assumed that the prior of scale parameters is a Beta-Gamma distribution and the prior of the common shape parameter is an independent Gamma distribution. Under squared error loss and LINEX loss functions, the Metropolis-Hastings algorithm is provided to compute the Bayes estimates and the credible intervals. Further, the statistical inferences with order restriction are studied when it is known a priori that the expectation of the lifespan of one population is shorter than that of the other population. A wide range of simulation experiments is conducted to evaluate the performance of the proposed methods. Finally, the lifetimes of white organic light-emitting diodes and the breaking strengths of jute fiber of gauge lengths are analyzed to illustrate the practical application of the proposed model and methods. [ABSTRACT FROM AUTHOR]

This paper investigates the E-Bayesian and hierarchical Bayesian estimations of shape parameter and reliability function of Kumaraswamy generalized distribution based on upper record values. The classical estimation method is utilized to deduce the maximum likelihood estimation of unknown parameter and reliability function. Bayesian estimates are derived by using conjugate Gamma prior distributions under quadratic and general entropy loss functions. Furthermore, assuming that hyper-hyperparameters obey three prior distributions, the E-Bayesian estimates of unknown parameters and reliability functions are obtained. The hierarchical Bayesian estimates are obtained by using hierarchical prior distributions. We also explore some characteristics and size relationships of E-Bayesian and hierarchical Bayesian estimations. The performance of E-Bayesian, Hierarchical Bayesian, Bayesian, and maximum likelihood estimations is compared based on the minimum mean square error criterion. Finally, the proposed estimation methods are applied to evaluate the reliability of the specimen under ultrasonic fatigue testing, and the results align with their structures and profiles. [ABSTRACT FROM AUTHOR]

Considering that continuous numerical methods cannot accurately describe the physical characteristics of cracks and discontinuous numerical methods cannot reflect structural stiffness,a rigid body spring model is proposed in this paper to analyze the failure process of reinforcement concrete(RC) structures.In the proposed method,concrete is simulated by the rigid body spring model based on Voronoi diagram random generated mesh.Reinforcement is modeled as a series of bar elements and the bond-slip characteristics between reinforcing steel and concrete are also considered by introducing special linkage elements.The spring stiffness of concrete is determined from the uniaixal stress-strain curve of concrete,and the shear failure behavior of concrete is judged by the Mohr-Coulomb criterion.A home-made program based on FORTRAN Language is developed and used to analyze the failure processes of a Z-type component under direct shear loading and a RC beam under two-point loading.The comparison of numerical results and experimental results show that the proposed method can simulate cracking behavior of RC structures precisely,and can provide the physical characteristics of cracks.The ultimate strengths and load-deflection response of the test beam predicted by the proposed method are in good agreement with the experimental results,which means the proposed method is feasible and effective.